Simplify (12 + 9i)/3

Step by step

The question

Question: work out (12 + 9i)/3.

Remember: i is the square root of minus 1.

So i squared is minus 1.

1 Split the fraction

The bottom is a plain number: 3.

So each part on top is divided by it.

12/3, and 9i/3.

12/3 is 4.

9/3 is 3.

So the answer is 4 + 3i.

2 Check

Let's check: times 3 undoes divided by 3.

We get 12 + 9i again.

It works!

Let's look back.

First: split the fraction.

Last: check.